Background: As a high-performance functional material, stacked piezoelectric actuator can produce a displacement under the effect of changing voltage. Its advantages of fast response and easy operation make it widely applied in the precision structure field. However, its small displacement stroke and hysteresis nonlinearity affect the accuracy of the output.
Method: In order to enlarge the displacement of piezoelectric actuator and reduce the influence of hysteresis, this study designs a diamond-shaped amplifying mechanism to amplify the output of the piezoelectric actuator, and then develops a self-tuning fuzzy fractional-order PIλDμ controller for the high precision displacement control of the proposed amplifying mechanism. After analyzing the working principle and modeling the amplifying mechanism, the fractional-order PIλDμ control model of the proposed mechanism was built and discretized according to the theoretical base of the fractional calculus in time domain. What’s more, the fuzzy control algorithm was also introduced to achieve self-turning of parameters. Besides, the amplifying mechanism was also adopted for a micro-droplet jetting dispenser to verify the practicability of the mechanism and control strategy.
In the next step, some experiments were undertaken based on the constructed platform.
Results: Experiments show that the displacement overshoots, the times of reaching steady state of the traditional integer-order controller and the fractional-order controller are 5.08%, 1.17% and 17.25 s, 12.00 s, respectively. However, the fuzzy PIλDμ controller lowers the overshoot and the time of reaching steady state to 0.95% and 9.00 s, respectively. The control algorithm can not only improve the follow-ability of the output displacement of the proposed mechanism, but also maintain the deviation within the range of 0.4% after the displacement stroke is stable and reduce the entering time of the mechanism up to 47.8%. In actual application, the droplet volume of micro-droplet jetting dispenser under fuzzy fractional-order PID control method is more stable, and its repeatability accuracy can reach up to 1.6475%.
Conclusion: Experimental results indicate that the self-tuning fuzzy fractional-order PIλDμ controller can significantly improve the tracking performances of the PID and the integer-order PID with regard to the amplifying mechanism with the advantages of good dynamic character and regulation precision. Furthermore, the diamond-shaped amplification mechanism and control strategy can be applied for some micro-droplet jetting dispensers used in microelectronic packaging, life science and 3D printing fields.